1/4x+36=-8.5x-40

Solution for 1/4x+36=-8.5x-40 equation:

1/4x+36=-8.5x-40

We move all terms to the left:

1/4x+36-(-8.5x-40)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x+8.5x+40+36=0

We multiply all the terms by the denominator


(8.5x)*4x+40*4x+36*4x+1=0

We add all the numbers together, and all the variables

(+8.5x)*4x+40*4x+36*4x+1=0

We multiply parentheses

32x^2+40*4x+36*4x+1=0

Wy multiply elements

32x^2+160x+144x+1=0

We add all the numbers together, and all the variables

32x^2+304x+1=0

a = 32; b = 304; c = +1;
Δ = b2-4ac
Δ = 3042-4·32·1
Δ = 92288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{92288}=\sqrt{64*1442}=\sqrt{64}*\sqrt{1442}=8\sqrt{1442}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(304)-8\sqrt{1442}}{2*32}=\frac{-304-8\sqrt{1442}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(304)+8\sqrt{1442}}{2*32}=\frac{-304+8\sqrt{1442}}{64}
$